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4. Solving Systems of Equations in Three Variables Applications and Mathematical Models Systems of Equations in Three Variables Systems of Equations and Matrices > Systems of Equations in Three Variables Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_41&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. A system of equations may have no solutions, one unique solution, or infinitely many solutions. The substitution method involves solving for one of the variables in one of the equations, and plugging that into the rest of the equations to reduce the system. Rinse and repeat until there is a single equation left, and then using this go backwards to solve the previous equations. The graphical method involves graphing all of the equations and finding points, lines or planes where all of the equations intersect at once, such points, lines or planes are the solutions. The elimination method involves adding or subtracting multiples of one equation from the other equations, eliminating variables from each of the equations until one variable is left in each equation (if there is a unique solution). Solving Systems of Equations in Three Variables Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/systems-of-equations-and-matrices-6/systems-of-equations-in-three- variables-41/solving-systems-of-equations-in-three-variables-194- 5835?campaign_content=book_196_section_41&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess System of Linear Equations View on Boundless.com Systems of Equations and Matrices > Systems of Equations in Three Variables

6. When you have multiple unknown quantities with multiple observations on these quantities and their interactions with each other, then the problem can usually be naturally described with a system of equations. When a system of equations is laid out, all of the equations need to be satisfied in order for there to be a solution. Sometimes there are no solutions; other times there are infinitely many solutions. There are numerous applications for systems of equations, such as Physics problems that involve multiple objects with multiple observations, or multiple forces that all need to be balanced. Applications and Mathematical Models Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/systems-of-equations-and-matrices-6/systems-of-equations-in-three- variables-41/applications-and-mathematical-models-195- 5887?campaign_content=book_196_section_41&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Physics Example: Second Observation View on Boundless.com Systems of Equations and Matrices > Systems of Equations in Three Variables

7. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

8. Key terms constraint A condition that a solution to a problem must satisfy. linear equation A polynomial equation of the first degree (such as x = 2y - 7). system of equations A set of equations with multiple variables which can be solved using a specific set of values. Free to share, print, make copies and changes. Get yours at www.boundless.com Systems of Equations and Matrices

9. System of Linear Equations This images shows a system of three equations in three variables. The intersecting point is the unique solution to this system. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Secretsharing-3-point." GNU FDL http://en.wikipedia.org/wiki/File:Secretsharing-3-point.png View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/File:Secretsharing-3-point.pngView on Boundless.com Systems of Equations and Matrices

10. Physics Example: First Observation Here is the first observation of three balls, two with unknown weight, which are balanced on a bar in a given configuration. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. "Linalg balance 1." CC BY-SA http://commons.wikimedia.org/wiki/File:Linalg_balance_1.png View on Boundless.comCC BY-SAhttp://commons.wikimedia.org/wiki/File:Linalg_balance_1.pngView on Boundless.com Systems of Equations and Matrices

11. Physics Example: Second Observation Here is the second observation of three balls, two with unknown weight, which are balanced on a bar in a given configuration. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. "Linalg balance 2." CC BY-SA http://commons.wikimedia.org/wiki/File:Linalg_balance_2.png View on Boundless.comCC BY-SAhttp://commons.wikimedia.org/wiki/File:Linalg_balance_2.pngView on Boundless.com Systems of Equations and Matrices

12. Free to share, print, make copies and changes. Get yours at www.boundless.com Systems of Equations and Matrices The admission fee at a museum is $1.50 for children and $4.00 for adults. On a Saturday, 2200 people entered the museum and $5050 was collected. How many children and how many adults went to the museum on Saturday? A) 1500 children and 700 adults B) 1600 children and 600 adults C) 1900 children and 300 adults D) 1800 children and 400 adults

13. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Systems of Equations and Matrices The admission fee at a museum is $1.50 for children and $4.00 for adults. On a Saturday, 2200 people entered the museum and $5050 was collected. How many children and how many adults went to the museum on Saturday? A) 1500 children and 700 adults B) 1600 children and 600 adults C) 1900 children and 300 adults D) 1800 children and 400 adults

14. Free to share, print, make copies and changes. Get yours at www.boundless.com Systems of Equations and Matrices A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? A) 15 B) 20 C) 5 D) 10

15. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Systems of Equations and Matrices A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? A) 15 B) 20 C) 5 D) 10

16. Attribution Wikibooks. "Linear Algebra/Solving Linear Systems." CC BY-SA 3.0 http://en.wikibooks.org/wiki/Linear_Algebra/Solving_Linear_SystemsCC BY-SA 3.0 http://en.wikibooks.org/wiki/Linear_Algebra/Solving_Linear_Systems Wikipedia. "System of equations." CC BY-SA 3.0 http://en.wikipedia.org/wiki/System_of_equationsCC BY-SA 3.0http://en.wikipedia.org/wiki/System_of_equations Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//algebra/definition/system-of-equationsCC BY-SA 3.0http://www.boundless.com//algebra/definition/system-of-equations Wikipedia. "System of equations." CC BY-SA 3.0 http://en.wikipedia.org/wiki/System_of_equationsCC BY-SA 3.0http://en.wikipedia.org/wiki/System_of_equations Wikibooks. "Linear Algebra/Solving Linear Systems." CC BY-SA 3.0 http://en.wikibooks.org/wiki/Linear_Algebra/Solving_Linear_SystemsCC BY-SA 3.0 http://en.wikibooks.org/wiki/Linear_Algebra/Solving_Linear_Systems Wiktionary. "linear equation." CC BY-SA 3.0 http://en.wiktionary.org/wiki/linear+equationCC BY-SA 3.0http://en.wiktionary.org/wiki/linear+equation Wiktionary. "constraint." CC BY-SA 3.0 http://en.wiktionary.org/wiki/constraintCC BY-SA 3.0http://en.wiktionary.org/wiki/constraint Free to share, print, make copies and changes. Get yours at www.boundless.com Systems of Equations and Matrices